(Vertigo/DC)
The Devil has made himself known throughout the history of DC. However, it is Neil Gaiman, Sam Keith, and Mike Dringenberg that can be credited with fleshing out the entity as Lucifer Morningstar in The Sandman #4 (1989).
Gaiman and company's Lucifer is weary of his aeons running Hell, which was supposedly a gift from God (but not so much). He eventually quits...relinquishing his wings and the Key to Hell to Morpheus and heading for Australia, then Los Angeles. In Los Angeles, he becomes owner of a nightclub, The Lux (lux- a measurement of luminance).
The Sandman series is definitely worth a read (I've shamelessly plugged it a number of times, here on Vingle) and so are "The Sandman Presents: Lucifer" and "Lucifer: Nirvana". And as much as I love my Neil Gaiman, Mike Carey is an equally compelling writer.
Carey's arc tears Lucifer away from his piano-playing and business operations to prevent a peculiar, wish-granting power from throwing the world into catastrophe. In return, the Voice of God says he will be granted whatever payment he wishes (o, sweet irony). Lucifer proceeds to tear through creation like you would expect a no-holds barred, pissed off fallen angel, with his greatest desire hanging in the balance.
The artwork changes flavor throughout the series, due to the shuffling of artists. I preferred Chris Weston's illustrations over those of Peter Gross and Dean Ormston, as his had a bit more flair and emotional depth. However, Mike Carey's story is engaging enough that it isn't too distracting or detracting.
I would recommend "Lucifer" for anyone who likes to explore philosophical matters or anyone who just loves their antiheroes (I know I do!)
P.S. If you are already a "Lucifer" fan, you will probably be excited to learn that Fox will be airing a new TV series based on the comics. Premieres Monday, January 25, 2016. SQUEEEEEE!!!!!

I was just talking to a friend about the show and came looking for this card again, @BeannachtOraibh. You Should be excited. The lead actor is EXQUISITE. We saw him in something a little while back and just Loved him. Really happy! And don't feel bad...I squee EVERY time I see the trailer. Lol ^_^

@ButterflyBlu I have been too...except one time last night when I was like "But Sandman hasn't gotten his own show yet"...felt sad for like two seconds, then I was like "Maybe he and Death will make appearances and get a spin-off"...which is bass ackwards, but works for me! XD